The precession frequencies at ambient pressure, \(f^{\rm AF}_1=45.37\)  MHz and \(f^{\rm AF}_2=92.99\)  MHz are fully consistent with our previous studies [1]}. When a hydrostatic pressure \(p=20\)  kbar is applied (i.e. compression of the lattice), the value of both \(f^{\rm AF}_1\)  and \(f^{\rm AF}_2\)  increases (see Fig. REF ), which is coherent with the TF results showing an increase in \(T_{\rm N}\) . Such results are summarized in Fig. REF (a). An increase in the values of precession frequency, implies an increase in the ordered moment and supports a scenario in which \(J_\perp \)  increases in strength with pressure application. This is also very reasonable when considering the NaFePO\(_4\)  sister compound mentioned above, which displays a larger Fe-Fe distance, and as a result, slightly lower \(T_{\rm N}\)  [2]}. Several high pressure studies of the atomic structure in LFPO have been published and there is some controversy in the results. An early high pressure XRD investigation reported a structural transition to a space group \(Cmcm\)  at a critical pressure below 65 kbar [3]}. However, other studies [4]} indicate a much higher critical pressure. Further, theoretical calculations based on the \(Cmcm\)  structure predict a decrease in the ordered Fe magnetic moment [5]} with applied pressure, as shown in Fig. REF (b). Our experimental result on the contrary show stronger magnetic correlations with applied pressure. Therefore, we may at least conclude that the supposed structural transition is not present up to 20 kbar. Our TF and ZF result also indicate that the spin structure at ambient pressure is most likely preserved up to at least \(p=20\)  kbar. We can of course not fully exclude a combination of atomic lattice compression together with a subtle change in the spin canting occurs. However, to discern such in-depth information, it would be necessary to conduct additional and detailed high-pressure neutron diffraction studies.
